Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings

Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings

Convergence of Set-valued Mappings: Equi-outer Semicontinuity

The concept of equi-outer semicontinuity allows us to relate the pointwise and the graphical convergence of set-valued-mappings. One of the main results is a compactness criterion that extends the classical Arzelà-Ascol̀ı Theorem for continuous functions to this new setting; it also leads to the exploration of the notion of continuous convergence. Equi-lower semicontinuity of functions is relate...

Convergence Theorems for Set-valued Denjoy-pettis Integrable Mappings

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.

Fixed Point Results for Multi-valued Non-expansive Mappings on an Unbounded Set

Some results regarding the existence of a fixed point for a multivalued non-expansive mapping defined on an unbounded subset of a reflexive Banach space are established.

Weighted Variational Inequalities with Set-valued Mappings

Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...